vdirectioner3847
07.03.2020 •
Mathematics
A geologist has collected 17 specimens of basaltic rock and 17 specimens of granite. The geologist instructs a laboratory assistant to randomly select 29 of the specimens for analysis.
a. What is the pmf of the number of granite specimens selected for analysis?
b. What is the probability that all specimens of one of the two types of rock are selected for analysis?
c. What is the probability that the number of granite specimens selected for analysis is within 1 standard deviation of its mean value?
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Ответ:
Step-by-step explanation:
Out of N = 34specimens, K = 17 are granite and 17 are basaltic.
Let X be the number of specimens that are granite in randomly selected n = 29 specimens
Tthe geometric random variable can only take integer values in range ; [max ( 0 , n + K - N), min (n, K )] = [ 12, 17] using the combination method;
nCr = n!/(n - r) r)! which is as shown below.
a)
XP(X)
120.0222
130.1454
140.3324
150.3324
160.1454
170.0222
b) P (all specimens of one of the two types of rock are selected for analysis
= C(17,17) x C (17,12) / C34,29) + C(17,12) x C (17,17) / C34,29) = 0.0445
c) Sample size, n = 29
No. of events of interest in population , k = 17Population size , N = 34mean = E(X) = n(k/N) = 14.5variance = nk(N-k)(N-n)/(N²(N-1)) = 1.0985Therefore, the probability that the number of granite specimens selected is within 1 standard deviation of mean ;
P (µ-σ < X < µ+σ) = P(14.5-1.05 < X <14.5+1.05) = P(13.45 < X <15.55) = P(X=14) + P(X=15) = 0.3324 + 0.3324 = 0.6647
Ответ:
the answer is b, hope this : )